The arctic circle boundary and the Airy process
arXiv:math/0306216 · doi:10.3189/172756405781813708
Abstract
We prove that the, appropriately rescaled, boundary of the north polar region in the Aztec diamond converges to the Airy process. The proof uses certain determinantal point processes given by the extended Krawtchouk kernel. We also prove a version of Propp's conjecture concerning the structure of the tiling at the center of the Aztec diamond.
Published at http://dx.doi.org/10.1214/009117904000000937 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
References in corpus (6)
- Discrete polynuclear growth and determinantal processes
- Local statistics of lattice dimers
- Scale Invariance of the PNG Droplet and the Airy Process
- A PDE for the joint distributions of the Airy Process
- Step fluctuations for a faceted crystal
- Uniform Asymptotics for Polynomials Orthogonal With Respect to a General Class of Discrete Weights and Universality Results for Associated Ensembles: Announcement of Results